Boy, they DO drive you crazy, don't they??!!! I'm trying to learn to cope with them myself. It was great when I finally got to see a doctor who has them himself (and he's healthy - just happens to be in the ectopic beat club) - he actually understood what a nightmare they can be (unfortunately I can't see him regularly - he's not on my insurance list - figures!!)
I don't think high cholesterol in and of itself can cause PVCs - but high cholesterol can contribute to coronary artery disease, which can cause them - but I doubt that's what's happening in your case, since your doctor would have likely explored that further if there were indications (gosh, I would hope so). The fact that you've never had your cholesterol checked made me guess you're quite young? I can't think of another setting where a doctor would treat you for high blood pressure and palps, and not check your cholesterol.
Do your PVCs get worse with exercise? If not, then that's a really good indication that they're perfectly harmless (except what they do to your mental state!) Even if they do get worse with exercise, it's not necessarily bad (mine did, but turned out to be benign PACs)
What does your doctor have to say about it? Are you seeing a cardiologist or EP doc? It's troubling to hear that you're taking a drug that's not helping you. Your doctor should be addressing this, seems to me.
You're certainly not alone - hope you feel better soon!